Generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis

Microbial Cells as a Microrobots: From Drug Delivery to Advanced Biosensors

The presented review focused on the microbial cell based system. This approach is based on the application of microorganisms as the main part of a robot that is responsible for the motility, cargo shipping, and in some cases, the production of useful chemicals. Living cells in such microrobots have both advantages and disadvantages. Regarding the advantages, it is necessary to mention the motility of cells, which can be natural chemotaxis or phototaxis, depending on the organism. There are approaches to make cells magnetotactic by adding nanoparticles to their surface. Today, the results of the development of such microrobots have been widely discussed. It has been shown that there is a possibility of combining different types of taxis to enhance the control level of the microrobots based on the microorganisms' cells and the efficiency of the solving task. Another advantage is the possibility of applying the whole potential of synthetic biology to make the behavior of the cells more controllable and complex. Biosynthesis of the cargo, advanced sensing, on/off switches, and other promising approaches are discussed within the context of the application for the microrobots. Thus, a synthetic biology application offers significant perspectives on microbial cell based microrobot development. Disadvantages that follow from the nature of microbial cells such as the number of external factors influence the cells, potential immune reaction, etc. They provide several limitations in the application, but do not decrease the bright perspectives of microrobots based on the cells of the microorganisms.

Smart micro- and nanorobots for water purification

Less than 1% of Earth's freshwater reserves is accessible. Industrialization, population growth and climate change are further exacerbating clean water shortage. Current water-remediation treatments fail to remove most pollutants completely or release toxic by-products into the environment. The use of self-propelled programmable micro- and nanoscale synthetic robots is a promising alternative way to improve water monitoring and remediation by overcoming diffusion-limited reactions and promoting interactions with target pollutants, including nano- and microplastics, persistent organic pollutants, heavy metals, oils and pathogenic microorganisms. This Review introduces the evolution of passive micro- and nanomaterials through active micro- and nanomotors and into advanced intelligent micro- and nanorobots in terms of motion ability, multifunctionality, adaptive response, swarming and mutual communication. After describing removal and degradation strategies, we present the most relevant improvements in water treatment, highlighting the design aspects necessary to improve remediation efficiency for specific contaminants. Finally, open challenges and future directions are discussed for the real-world application of smart micro- and nanorobots.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Phototaxis of Chlamydomonas arises from a tuned adaptive photoresponse shared with multicellular Volvocine green algae

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.

Long-time behavior of swimming Euglena gracilis in a heterogenous light environment

The cell motion of Euglena gracilis in homogeneous and heterogeneous light environments was analyzed. Homogeneous and heterogeneous environments were prepared, with only a red color or with a red circle surrounded by brighter white regions, respectively. In a heterogeneous environment, the cells move into the red circle. Swimming orbits at 1/25 s intervals for 120 s were analyzed. The speed distribution of the 1 s-averaged cell orbits in a homogeneous environment was different from that in a heterogeneous environment, where the faster swimming fraction was enhanced. The relationship between speed and curvature radius was analyzed using a joint histogram. Histograms for short timescale motion, constructed by 1 s-averaged orbits, suggest that the cell swimming curves are not biased, while those for long timescale motion, constructed by 10 s-averaged orbits, suggest that the cell swimming curves are biased in the clockwise direction. Furthermore, the curvature radius determines the speed, which does not seem to depend on the light environment. The mean squared displacement in a heterogeneous environment is larger than that in a homogeneous environment on a 1 s timescale. These results will be the basis for constructing a model for the long-time behavior of photomovement for light differences.

Nonlinear Phototaxis and Instabilities in Suspensions of Light-Seeking Algae

The mechanism by which living organisms seek optimal light conditions-phototaxis-is a fundamental process for motile photosynthetic microbes. It is involved in a broad array of natural processes and applications from bloom formation to the production of high-value chemicals in photobioreactors. Here, we show that a population of the model alga Chlamydomonas reinhardtii exhibits a highly sensitive nonlinear response to light and demonstrate that the self-organization of cells in a heterogeneous environment becomes unstable as the result of a coupling between bioconvective flows and phototaxis.

Ecohydrology 2.0

This paper aims at a definition of the domain of ecohydrology, a relatively new discipline borne out of an intrusion-as advertised by this Topical Collection of the Rendiconti Lincei-of hydrology and geomorphology into ecology (or vice-versa, depending on the reader's background). The study of hydrologic controls on the biota proves, in our view, significantly broader than envisioned by its original focus that was centered on the critical zone where much of the action of soil, climate and vegetation interactions takes place. In this review of related topics and contributions, we propose a reasoned broadening of perspective, in particular by firmly centering ecohydrology on the fluvial catchment as its fundamental control volume. A substantial unity of materials and methods suggests that our advocacy may be considered legitimate.

Collective self-optimization of communicating active particles

The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource-such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins-while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared "resource field," the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.

Species Interactions Limit the Predictability of Community Responses to Environmental Change

AbstractPredicting how ecological communities will respond to environmental change is challenging but highly relevant in this era of global change. Ecologists commonly use current spatial relationships between species and environmental conditions to make predictions about the future. This assumes that species will track conditions by shifting their distributions. However, theory and experimental evidence suggest that species interactions prevent communities from predictably tracking temporal changes in environmental conditions on the basis of current spatial relationships between species and environmental gradients. We tested this hypothesis by assessing the dynamics of protist species in replicated two-patch microcosm landscapes that experienced different regimes of spatial and temporal environmental heterogeneity (light vs. dark). Populations were kept in monocultures or polycultures to assess the effect of species interactions. In monocultures, abundances were predictable on the basis of current environmental conditions, regardless of whether the populations had experienced temporal environmental change. But in polycultures, abundances also depended on the history of the environmental conditions experienced. This suggests that because of species interactions, communities should respond differently to spatial versus temporal environmental changes. Thus, species interactions likely reduce the accuracy of predictions about future communities that are based on current spatial relationships between species and the environment.

Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism’s movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms’ population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.

Can playing Spirograph lead to an ordered structure in self-propelled particles?

Understanding the local dynamics of microorganisms infecting a cell could help us develop efficient strategies to counter their aggregation. In the present study we have introduced a simple model of self-propelled particles (SPPs) with constant linear velocity, both in 2 and 3 dimensions, which captures the essential features of a microorganism's aggregation as well the dynamics around an attractive point (AP). The static behavior shows the presence of an icosahedral structure for a finite number of SPPs, and a hexagonal closed packed structure for an infinite number of SPPs, which was confirmed using Steinhardt bond order parameters for a 3-dimensional model. For a single SPP the dynamic behaviour involves the formation of orbits around the AP, which can be categorised into three dynamical regions based on the strength of coupling between the AP and SPP. For weak coupling we observe a rosette-like trajectory reminiscent of the pattern formed by the Spirograph toy. For intermediate coupling, circular trajectories were observed, and for very strong coupling the SPP was static and was always aligned with the AP. The radial distance from the AP to SPP was determined by the angular velocities of the SPP for the rosette-like region whereas for the circular and static regions, it was determined by the coupling constant. Even for a finite number of SPPs we observed the same behavior as long as the SPPs could rotate around the AP without colliding with each other.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

Controlling Cell Motion and Microscale Flow with Polarized Light Fields

We investigate how light polarization affects the motion of photoresponsive algae, Euglena gracilis. In a uniformly polarized field, cells swim approximately perpendicular to the polarization direction and form a nematic state with zero mean velocity. When light polarization varies spatially, cell motion is modulated by local polarization. In such light fields, cells exhibit complex spatial distribution and motion patterns which are controlled by topological properties of the underlying fields; we further show that ordered cell swimming can generate directed transporting fluid flow. Experimental results are quantitatively reproduced by an active Brownian particle model in which particle motion direction is nematically coupled to local light polarization.

Flagellum Malfunctions Trigger Metaboly as an Escape Strategy in Euglena gracilis

Euglenoids present the ability to alter the shape of their bodies, a process referred to as metaboly. Metaboly is usually used by phagotrophic cells to engulf their prey. However, Euglena gracilis is osmotrophic and photosynthetic. Though metaboly was discovered centuries ago, it remains unclear why E. gracilis undergo metaboly and what causes them to deform, and some consider metaboly to be a functionless ancestral vestige. Here, we discover that flagellum malfunctions trigger metaboly and metaboly is a smart escape strategy adopted by E. gracilis when the proper rotation and beating of the flagellum are hindered by restrictions including surface obstruction, sticking, resistance, or limited space. Metaboly facilitates escape in five ways: (i) detaching the body from the surface; (ii) enlarging the space between flagellum and the restricting surface which restores beating and rotation of the flagellum; (iii) decreasing the torque of viscous resistance for rotation of the body; (iv) decreasing the length of the body; and (v) crawling backwards on a surface or swimming backwards if the flagellum completely malfunctions or has broken off. Our findings suggest that metaboly plays a key role in enabling E. gracilis to escape from harmful conditions when flagellar functions are impaired or absent.

Photo-bioconvection: towards light control of flows in active suspensions

The persistent motility of individual constituents in microbial suspensions represents a prime example of the so-called active matter systems. Cells consume energy, exert forces and move, overall releasing the constraints of equilibrium statistical mechanics of passive elements and allowing for complex spatio-temporal patterns to emerge. Moreover, when subject to physico-chemical stimuli their collective behaviour often drives large-scale instabilities of a hydrodynamic nature, with implications for biomixing in natural environments and incipient industrial applications. In turn, our ability to exert external control of these driving stimuli could be used to govern the emerging patterns. Light, being easily manipulable and, at the same time, an important stimulus for a wide variety of microorganisms, is particularly well suited to this end. In this paper, we will discuss the current state, developments and some of the emerging advances in the fundamentals and applications of light-induced bioconvection with a focus on recent experimental realizations and modelling efforts. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Quantitative analysis of the gain in probability of escaping for ideal phototactic swimmers due to chaotic dynamics

We study the dynamics of ideal phototactic swimmers in a steady two-dimensional model flow with transport barriers. We consider a distant light source, in which case the self-propulsion velocity of the swimmers is, at any instant, along a predetermined direction. The probability of transport along that direction emerges from the competing effects of the swimmers' self-propulsion and the flow's transport barriers. For swimmers bounded to have the same time average self-propulsion speed, temporal modulation of that speed increases the probability of escaping due to the formation of a stochastic layer which fosters transport. We use separatrix-map techniques to calculate the gain in the probability of escaping.

Disturbance of chiral ionic liquids to phototaxis of Chlamydomonas reinhardtii: regular analysis and mechanism attempt

Given the recent extensive synthesis and application of ionic liquids (ILs), finding a sensitive and visual indicator to provide a fast-initial risk assessment of IL use has become a pressing issue. In this study, we verified that the phototaxis of Chlamydomonas reinhardtii is a valid indicator of the environmental risk associated with chiral ILs L-(+)- and D-(-)-1-butyl-3-methylimidazolium lactate (BMIM L). Briefly, C. reinhardtii was exposed to a 4000-lx side light source for varying lengths of time. Following the allotted exposure time, the algae aggregation was photographed, and then quantitative analysis was conducted using Image-J software to obtain the corresponding relationship between IL stimulation and C. reinhardtii phototaxis. The gray areas from each treatment were measured and the percentage was calculated. After 16 h of side lighting, for control, the percentage of gray areas was - 22%, while for L-(+)- and D-(-)- BMIM L were 17% and 33%, respectively. Then, after 8 h of darkness, where D-(-)-BMIM L and the control showed the positive phototaxis, but the L-(+)-BMIM L-treated group showed virtually no change. This phenomenon is consistent with excessive production of reactive oxygen species (ROS). Moreover, atomic force microscope (AFM) results indicated distinct aggregation between D-(-)- and L-(+)-BMIM L, which caused changes in cell permeability that induced a change in ROS transfer. Furthermore, relationship between phototaxis and changes in cell ultrastructure and photosynthetic efficiency was also investigated. This work demonstrates the potential of phototaxis to serve as a sensitive, convenient, and cost effective qualitative assessment of ILs' toxic impact, with the understanding that quantitative evaluation requires further improvement.

Biofilms at interfaces: microbial distribution in floating films

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Mechanism Underlying Flow Velocity and Its Corresponding Influence on the Growth of Euglena gracilis, a Dominant Bloom Species in Reservoirs

The effects of hydrodynamics on algae growth have received considerable attention, and flow velocity is one of the most frequently discussed factors. For Euglena gracilis, which aggregates resources and is highly resistant to environmental changes, the mechanism underlying the impact of flow velocity on its growth is poorly understood. Experiments were conducted to examine the response of algae growth to different velocities, and several enzymes were tested to determine their physiological mechanisms. Significant differences in the growth of E. gracilis were found at different flow velocities, and this phenomenon is unique compared to the growth of other algal species. With increasing flow velocity and time, the growth of E. gracilis is gradually inhibited. In particular, we found that the pioneer enzyme is peroxidase (POD) and that the main antioxidant enzyme is catalase (CAT) when E. gracilis experiences flow velocity stress. Hysteresis between total phosphorus (TP) consumption and alkaline phosphatase (AKP) synthesis was observed. Under experimental control conditions, the results indicate that flow velocities above 0.1 m/s may inhibit growth and that E. gracilis prefers a relatively slow or even static flow velocity, and this finding could be beneficial for the control of E. gracilis blooms.

Light Control of Localized Photobioconvection

Microorganismal motility is often characterized by complex responses to environmental physico-chemical stimuli. Although the biological basis of these responses is often not well understood, their exploitation already promises novel avenues to directly control the motion of living active matter at both the individual and collective level. Here we leverage the phototactic ability of the model microalga Chlamydomonas reinhardtii to precisely control the timing and position of localized cell photoaccumulation, leading to the controlled development of isolated bioconvective plumes. This novel form of photobioconvection allows a precise, fast, and reconfigurable control of the spatiotemporal dynamics of the instability and the ensuing global recirculation, which can be activated and stopped in real time. A simple continuum model accounts for the phototactic response of the suspension and demonstrates how the spatiotemporal dynamics of the illumination field can be used as a simple external switch to produce efficient bio mixing.

The dialogue between protozoa and bacteria in a microfluidic device

In nature, protozoa play a major role in controlling bacterial populations. This paper proposes a microfluidic device for the study of protozoa behaviors change due to their chemotactic response in the presence of bacterial cells. A three-channel microfluidic device was designed using a nitrocellulose membrane into which channels were cut using a laser cutter. The membrane was sandwiched between two glass slides; a Euglena suspension was then allowed to flow through the central channel. The two side channels were filled with either, 0.1% peptone as a negative control, or a Listeria suspension respectively. The membrane design prevented direct interaction but allowed Euglena cells to detect Listeria cells as secretions diffused through the nitrocellulose membrane. A significant number of Euglena cells migrated toward the chambers near the bacterial cells, indicating a positive chemotactic response of Euglena toward chemical cues released from Listeria cells. Filtrates collected from Listeria suspension with a series of molecular weight cutoffs (3k, 10k and 100k) were examined in Euglena chemotaxis tests. Euglena cells were attracted to all filtrates collected from the membrane filtration with different molecular weight cutoffs, suggesting small molecules from Listeria might be the chemical cues to attract protozoa. Headspace volatile organic compounds (VOC) released from Listeria were collected, spiked to 0.1% peptone and tested as the chemotactic effectors. It was discovered that the Euglena cells responded quickly to Listeria VOCs including decanal, 3,5- dimethylbenzaldehyde, ethyl acetate, indicating bacterial VOCs were used by Euglena to track the location of bacteria.

Reentrant Efficiency of Phototaxis in Chlamydomonas reinhardtii Cells

Phototaxis is one of the most fundamental stimulus-response behaviors in biology wherein motile microorganisms sense light gradients to swim toward the light source. Apart from single-cell survival and growth, it plays a major role at the global scale of aquatic ecosystems and bioreactors. We study phototaxis of single-celled algae Chlamydomonas reinhardtii as a function of cell number density and light stimulus using high spatiotemporal video microscopy. Surprisingly, the phototactic efficiency has a minimum at a well-defined number density, for a given light gradient, above which the phototaxis behavior of a collection of cells can even exceed the performance obtainable from single isolated cells. We show that the origin of enhancement of performance above the critical concentration lies in the slowing down of the cells, which enables them to sense light more effectively. We also show that this steady-state phenomenology is well captured by modeling the phototactic response as a density-dependent torque acting on an active Brownian particle.

Theory of light-activated catalytic Janus particles

We study the dynamics of active Janus particles that self-propel in solution by light-activated catalytic decomposition of chemical "fuel." We develop an analytical model of a photo-active self-phoretic particle that accounts for "self-shadowing" of the light by the opaque catalytic face of the particle. We find that self-shadowing can drive "phototaxis" (rotation of the catalytic cap toward the light source) or "anti-phototaxis," depending on the properties of the particle. Incorporating the effect of thermal noise, we show that the distribution of particle orientations is captured by a Boltzmann distribution with a nonequilibrium effective potential. Furthermore, the mean vertical velocity of phototactic (anti-phototactic) particles exhibits a superlinear (sublinear) dependence on intensity. Overall, our findings show that photo-active particles exhibit a rich "tactic" response to light, which could be harnessed to program complex three-dimensional trajectories.

Phototaxis of active colloids by self-thermophoresis

Phototaxis usually refers to the ability of a motile micoorganism to move directionally within a light gradient, which is important for microorganisms to gain energy or avoid damage. Here, we show that an active Janus particle driven by self-thermophoresis from light heating is able to exhibit significant phototactic motion by means of mesoscale dynamics simulation. Depending on the particle-fluid interactions, the active particle can move along or against the light gradient, corresponding to positive or negative phototaxis, respectively. We find that the phototaxis of the active colloid is determined by various mechanisms, including alignment (polarization) of the particle to the light gradient, orientation-dependent motility and spatially inhomogeneous motility. Our results shed light on the phototactic behavior of artificial active colloids and open up a new possibility to design photo-responsive micromachines.

Viscotaxis: Microswimmer Navigation in Viscosity Gradients

The survival of many microorganisms, like Leptospira or Spiroplasma bacteria, can depend on their ability to navigate towards regions of favorable viscosity. While this ability, called viscotaxis, has been observed in several bacterial experiments, the underlying mechanism remains unclear. We provide a framework to study viscotaxis of biological or synthetic self-propelled swimmers in slowly varying viscosity fields and show that suitable body shapes create viscotaxis based on a systematic asymmetry of viscous forces acting on a microswimmer. Our results shed new light on viscotaxis in Spiroplasma and Leptospira and suggest that dynamic body shape changes exhibited by both types of microorganisms may have an unrecognized functionality: to prevent them from drifting to low viscosity regions where they swim poorly. The present theory classifies microswimmers regarding their ability to show viscotaxis and can be used to design synthetic viscotactic swimmers, e.g., for delivering drugs to a target region distinguished by viscosity.

Nonlinear population dynamics in a bounded habitat

A key issue in ecology is whether a population will survive long term or go extinct. This is the question we address in this paper for a population in a bounded habitat. We will restrict our study to the case of a single species in a one-dimensional habitat of length L. The evolution of the population density distribution ρ(x, t), where x is the position and t the time, is governed by elementary processes such as growth and dispersal, which, in standard models, are typically described by a constant per capita growth rate and normal diffusion, respectively. However, feedbacks in the regulatory mechanisms and external factors can produce density-dependent rates. Therefore, we consider a generalization of the standard evolution equation, which, after dimensional scaling and assuming large carrying capacity, becomes ∂_tρ=∂_x(ρ^ν-1∂_xρ)+ρ^μ, where μ,ν∈R. This equation is complemented by absorbing boundaries, mimicking adverse conditions outside the habitat. For this nonlinear problem, we obtain, analytically, exact expressions of the critical habitat size L_c for population survival, as a function of the exponents and initial conditions. We find that depending on the values of the exponents (ν, μ), population survival can occur for either L ≥ L_c, L ≤ L_c or for any L. This generalizes the usual statement that L_c represents the minimum habitat size. In addition, nonlinearities introduce dependence on the initial conditions, affecting L_c.

Modeling of active swimmer suspensions and their interactions with the environment

In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

Phototaxis beyond turning: persistent accumulation and response acclimation of the microalga Chlamydomonas reinhardtii

Phototaxis is an important reaction to light displayed by a wide range of motile microorganisms. Flagellated eukaryotic microalgae in particular, like the model organism Chlamydomonas reinhardtii, steer either towards or away from light by a rapid and precisely timed modulation of their flagellar activity. Cell steering, however, is only the beginning of a much longer process which ultimately allows cells to determine their light exposure history. This process is not well understood. Here we present a first quantitative study of the long timescale phototactic motility of Chlamydomonas at both single cell and population levels. Our results reveal that the phototactic strategy adopted by these microorganisms leads to an efficient exposure to light, and that the phototactic response is modulated over typical timescales of tens of seconds. The adaptation dynamics for phototaxis and chlorophyll fluorescence show a striking quantitative agreement, suggesting that photosynthesis controls quantitatively how cells navigate a light field.

The Flux of Euglena gracilis Cells Depends on the Gradient of Light Intensity

We have quantified the photomovement behavior of a suspension of Euglena gracilis representing a behavioral response to a light gradient. Despite recent measurements of phototaxis and photophobicity, the details of macroscopic behavior of cell photomovements under conditions of light intensity gradients, which are critical to understand recent experiments on spatially localized bioconvection patterns, have not been fully understood. In this paper, the flux of cell number density under a light intensity gradient was measured by the following two experiments. In the first experiment, a capillary containing the cell suspension was illuminated with different light intensities in two regions. In the steady state, the differences of the cell numbers in the two regions normalized by the total number were proportional to the light difference, where the light intensity difference ranged from 0.5-2.0 μmol m-2 s-1. The proportional coefficient was positive (i.e., the bright region contained many microorganisms) when the mean light intensity was weak (1.25 μmol m-2 s-1), whereas it was negative when the mean intensity was strong (13.75 μmol m-2 s-1). In the second experiment, a shallow rectangular container of the suspension was illuminated with stepwise light intensities. The cell number density distribution exhibited a single peak at the position where the light intensity was about Ic ≃ 3.8 μmol m-2 s-1. These results suggest that the suspension of E. gracilis responded to the light gradient and that the favorable light intensity was Ic.

Phototaxis of synthetic microswimmers in optical landscapes

Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light gradients can also be achieved in a system of synthetic photo-activated microparticles being exposed to an inhomogeneous laser field. We observe a strong orientational response of the particles because of diffusiophoretic torques, which in combination with an intensity-dependent particle motility eventually leads to phototaxis. Since the aligning torques saturate at high gradients, a strongly rectified particle motion is found even in periodic asymmetric intensity landscapes. Our results are in excellent agreement with numerical simulations of a minimal model and should similarly apply to other particle propulsion mechanisms. Because light fields can be easily adjusted in space and time, this also allows to extend our approach to dynamical environments.